It is common practice to extract air from the high pressure compressor flowpath either at the inlet or a subsequent compressor stage for introduction into the compressor bore to control the temperature of the compressor rotor. The objectives of this practice are to prevent localized heating and thus extend service life, to control the clearance between the rotor blade tips and the stator shrouds defining the outer bounds of the compressor flowpath, and to purge the rotor bore. Purging is required to reduce cavity windage and to remove high temperature air leaking into the compressor bore from the compressor flowpath. Typically, the extracted cooling air is metered into the upstream or forward end of the compressor bore, which then flows monotonically downstream through the bore, with mixing of the cooling air and the air existing in the cavities between rotor discs determined mainly by local flow conditions. Because the various compressor stage discs have different cooling requirements, the monotonic flow of extracted air through the compressor bore from forward to aft ends does not fully achieve these objectives.